abstract
The dynamics of a macroscopic grain rolling on an inclined plane composed
of fixed identical grains is investigated both experimentally and theoretically.
As real sand, the system exhibits an hysteretic transition between static
and dynamical states: for angles smaller than jd,
the roller always stops, for angles larger than js,
it spontaneously starts rolling down but for angles between jd
and js, it can be either
at rest, or in motion with a constant velocity. It is shown that the limit
velocity is given by the equilibrium between gravity driving and dissipation
by the shocks. Moreover, the rough plane acts as a periodic potential trap
whose width and depth decrease when the angle is increased: the static
angle corresponds to the angle for which the trap disappears; the dynamical
angle $\phi_d$ to that for which the limit velocity is sufficient to escape
from the trap. Finally, a continuous description of the force globally
acting on the grain is proposed, which preserves this hysteretic behaviour.